High-Precision Nonperturbative QCD

Transcription

1 High-Precision Nonperturbative QCD Peter Lepage Cornell University. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.1/77

2 Why High-Precision and Nonperturbative?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.2/77

3 Essential for Standard Model E.g., CKM weak interaction parameters ρ and η from: B- B mixing B πlν K- K mixing... Nonpert ve QCD Part Weak Int n Part. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.3/77

4 CKM today and with 2 3% theory errors. And with B Factories... 95% confidence levels; CLEO-c (2001).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.4/77

5 Essential Beyond the S.M.? Strongly coupled field theories are an outstanding challenge to all theoretical physics. Field theory is generic; weak coupling is not. 2 of 3 known interactions are strongly coupled: QCD, gravity.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.5/77

6 Asymptotic freedom + logarithmic evolution Strong coupling at low E and large mass hierarchies. E.g., in QCD: α s (M planck ) = 0.02 and α s (m hadron ) 1 m hadron /M planck Strong coupling is natural in particle physics.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.6/77

7 Strong coupling is possible (likely?) at the LHC and/or beyond. Generic at low energies in non-abelian gauge theories unless gauge symmetry spontaneously broken dynamical symmetry breaking strong coupling. Critical near-term need for reliable, generic techniques for strong coupling.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.7/77

8 What is Lattice QCD?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.8/77

9 Lattice Approximation Continuous Space & Time site a L Fields ψ(x), A µ (x) specified only at grid sites; interpolate for other points.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.9/77

10 QCD multidimensional integration. DA µ... e Ldt da µ (x j )... e a L j. x j ɛ grid Millions of integration variables. Numerical Monte Carlo integration. N.B. Cost (1/a) ω where ω 6 implies must keep a as large as possible!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.10/77

11 Fall & Rise of LQCD Invented in 1974; explains confinement. Stalls for almost 20 years. Ken Wilson declares it dead! (1989) Renaissance in 1990 s. Perturbation theory fixed. Effective field theories for c, b s. Improved discretizations larger a s. Unquenching! (2000) First high-prescision nonperturbative results. α s (M Z ), M b... to few %. Ken Wilson retracts. (1995). G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.11/77

12 QCD Revolution Traditional wisdom New simulation results need a 0.05 fm. a = fm works. Simulation cost (1/a) 6 new simulations cost times less!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.12/77

13 Quantum Field Theory on a Lattice. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.13/77

14 Approximate Derivatives Numerical Analysis ψ(x j ) x = x ψ(x j ) + O(a 2 ) ψ(x j + a) ψ(x j a) 2a uses only ψ s at grid sites. N.B. Errors (pa) n want p < O(1/a).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.14/77

15 Large a need improved discretizations. E.g. ψ x = xψ a2 6 3 xψ + O(a 4 ) 10 15% for a = 0.4 fm 1 2% for a = 0.4 fm N.B. Need smaller as for large p. a = 0.4 fm okay?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.15/77

16 Ultraviolet Cutoff λ min = 2a is smallest wavelength. E.g.) ψ = all quark and gluon states with p > π/a are excluded by the lattice since p = 2π/λ. lattice QCD QCD + lattice UV regulator real QCD.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.16/77

17 But ps important in quantum field theory! (Consider ultraviolet divergences.) Renormalization Theory mimic effects of p > π/a excluded states by adding extra a-dependent local terms to the field equations, Lagrangian, currents, etc.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.17/77

18 ψ ψ + c(a) a 2 3 ψ + where c(a) = Contribution for p > π/a physics Numerical Analysis Theory & context specific not universal!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.18/77

19 Bad News: Need a 2 corrections when a large, but Numerical Recipes won t tell you values of c(a).... G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.19/77

20 Good News: p > π/a QCD is perturbative if a small enough (asymptotic freedom). compute c(a)... using perturbation theory. Perturbation theory fills in gaps in lattice; continuum results without a 0!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.20/77

21 E.g., Renormalization constant. L (a) = Z(a) ψ( γ m(a))ψ +c(a) a 2 ψ 3 γψ + where Finite-a correction. c(a) = c 1 α s (π/a) + Numerical Analysis Mimics effects of p > π/a states excluded by grid.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.21/77

22 Asymptotic freedom in QCD short-distance physics simple (perturbative); long-distance physics difficult (nonperturbative). Lattice separates short from long : p > π/a QCD corrections δl computed in perturbation theory (determines a); p < π/a QCD nonperturbative, numerical Monte Carlo integration.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.22/77

23 Perturbation Theory Improved discretizations and larger as old ideas. But perturbation theory is essential. a must be small enough so that p π/a QCD is perturbative. Before 1992: a < 0.05 fm. After 1992: a < 0.4 fm works.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.23/77

24 Test by comparing short-distance quantities from: perturbation theory; numerical Monte Carlo integration ( exact result). E.g., Wilson loops: W (C) Re Tr P e ig C A dx 0, C = small, closed path.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.24/77

25 χ 22 Loop Ratio 1 st Order 0.4 exact new P.Th. old P.Th. χ loop size (fm) χ 22 Loop Ratio 2 nd Order 0.4 exact new P.Th. old P.Th. χ loop size (fm). G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.25/77

26 Running coupling constant: α P (q 1,1 ) q 1,1 (GeV). G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.26/77

27 LQCD Tour. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.27/77

28 Recap Expect errors < few % from simulations with a < 0.4 fm. Improved discretizations essential for speed and precision. Questions: Do the improvements work? Are the simulations faster?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.28/77

29 Gluons Original discretization of the gluon action (Wilson, 1974) has O(a 2 ) errors: L Wil µ,ν { } 1 2 Tr F µν 2 + a2 24 Tr F µν(d 2 µ + D 2 ν)f µν. O(a 2 ) error violates rotation/poincaré invariance (due to lattice); removed by adding correction terms.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.29/77

30 4 a) Wilson Action a V (r) r/a 4 b) Improved Action a V (r) r/a. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.30/77

31 Quarks The standard discretization of the quark action has O(a 2 ) errors: L lat ψ(d γ + m)ψ + a2 6 µ ψd 3 µ γ µ ψ +. O(a 2 ) error violates rotation/poincaré invariance; removed by adding correction term.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.31/77

32 Test by computing c 2 (p) E2 (p) m 2 p 2 ; Lorentz invariance implies: c 2 (p) = 1 p.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.32/77

33 Improved D234c φ π s c 2 (p) SW π s 0.2 φ Standard pa Alford et al (1997).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.33/77

34 Heavy Quarks Lattice errors (a E) n, (a p) n need a 1/M where M = hadron mass. B, Υ... Need a a/10 Cost 10 6 cost! Impossible?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.34/77

35 No! b quark is nonrelativistic: v 2 2 M M 0.5 GeV 10 GeV v 2 0.1; don t use Dirac; use effective field theory. Schrödinger + O(a, a 2 ) corrections + O(v 2, v 4 ) corrections +.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.35/77

36 Lattice NRQCD: Schrödinger: Corrections: H 0 D2 2M 0 + ig A 0, δh (D 2 ) 2 ( c 1 8M am ) 0 2n g ig c 3 σ B + c 4 2M 0 c 5 g 8M 2 0 8M c 2 a 2 i D4 i 24M 0 σ (D E E D). (D E E D) where perturbation theory c i = 1 + c i1 α s (π/a) + ; only two parameters: α s and M 0.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.36/77

37 GeV S 0 3 S 1 1 P 1 1 D 2 Davies et al. (1997).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.37/77

38 MeV 20 χ b2 0 h b χ b χ b0 Davies et al. (1997).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.38/77

39 Tune two parameters to reproduce experimental data few % accurate results for M b and α MS (M Z ).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.39/77

40 Average Hadronic Jets e + e - rates e + e - event shapes Fragmentation Z width ep event shapes Polarized DIS Deep Inelastic Scattering (DIS) τ decays Lattice Υ decay α s (M Z ) Particle Data Group (2001).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.40/77

41 Unquenching. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.41/77

42 Unquenched LQCD Quenched QCD QCD without quark vacuum polarization % errors in most calculations; the major limitation of LQCD until vac. polarization. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.42/77

43 Naive/staggered quarks + improved discretization times faster & smallest finite-a errors & best behavior in chiral limit! high-precision (few %) LQCD possible now! MILC collaboration has already produced thousands of configurations: n f = 3; smallest (m u =m d ) ever: m s... m s /5, m s /7; small as: 1/8 fm, 1/11 fm; large Ls: 2.5 fm, 3.0 fm.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.43/77

44 Naive/Staggered Quarks Simplest discretization of light quarks, L = ψ(x)( γ + m)ψ(x) an exact doubling symmetry: ψ(x) ψ(x) iγ 5 γ ρ ( 1) xρ/a ψ(x) = iγ 5 γ ρ exp(i x ρ π/a) ψ(x). Any low-energy mode ψ Another mode, ψ, with p ρ π/a. max. p on lattice. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.44/77

45 General case: ψ(x) B ζ (x) ψ(x) where B ζ (x) ρ (iγ 5 γ ρ ) ζ ρ exp(i x ζ π/a) ζ = (1, 0, 0, 0), (0, 1, 0, 0)... (1, 1, 0, 0)..., 15 in all. 1 field ψ(x) creates 16 different but exactly equivalent flavors of quark (p ζπ/a)!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.45/77

46 16 flavors is bad! Two traditional options: 1. (Wilson, SW... ) Break doubling symmtry by adding aψ(d γ) 2 ψ/2 to L; destroys all chiral symmetry small m u,d very difficult. 2. (Kogut-Susskind... ) Live with the 16 flavors by inserting factors of 1/16 in strategic places. Preserves a chiral symmetry small masses relatively efficient. Follow option 2!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.46/77

47 E.g., 16 equivalent B mesons constructed from a b quark and 16 flavors of u antiquark: e.g., p u (0, 0, 0, 0) p u (π/a, 0, 0, 0) p b 0 p b 0 Ignore all but first (equivalent) by limiting total momentum: P B p b + p u < π 2a. P B distinguishes between flavors.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.47/77

48 Light hadrons harder. Bad News: Flavor-changing strong interactions p 0 p π/a p 0 p π/a Quarks on-shell, but different flavor. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.48/77

49 Good News: The gluon carries the largest lattice momentum, π/a; highly virtual and perturbative; can remove by (local) perturbative modifications to L to any order in α s (π/a). The new idea! Four quark operators + a 2 3 correction as before. Most accurate discretization. See Lepage (1998); MILC (1999).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.49/77

50 An amazing fact: Ω(x) µ (γ µ ) x µ/a S F (x, y; A µ ) = g(x, y; A µ ) Ω(x) Ω (y) Propagator. Dirac scalar for any gluon field A µ. Dirac structure is completely independent of A µ! times faster than all other alternatives!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.50/77

51 Domain-Wall Fermions An approach for chiral fermions? Embed 4-D space-time in 5-D: (x µ, s). Use Wilson lattice Dirac equation in 5-D, ( D γ + D s γ 5 a ) 2 (D2 + Ds) 2 + m(s) Ψ = 0, but with 1/a m(s) L s See Kaplan. (1992). G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.51/77

52 Separable chiral Ψ ±, such that D γ Ψ ± = 0, localized where m(s) = 0 domain walls: Ψ + Ψ s + hel. hel. Keep only s = 0 or L solution chiral theory wide range of new applications? Key issue: Do the two solutions communicate?. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.52/77

53 Why are Quarks so Hard? Anomalies!? Chiral symm. + massless quarks Quark helicity (±) is Lorentz invariant. µ j 5µ = 0 (classically) n + n conserved. No interaction in L changes to +. Quantum effects (anomaly) j 5 E B n + n can change!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.53/77

54 E.g., vacuum Fermi levels shift as E B varies: Energy Energy Continuum: 0 + n + n > 0 + Energy Lattice?? π/a Too few particles. Too many particles.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.54/77

55 Energy Naive/Staggered Quarks: n + n = 0, still; anomalies cancel between flavors. π/2a p 0 p π/a Energy Domain Wall Quarks: 0 + Particles move from to + via 5th dimension. s = 0 s = L. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.55/77

56 Near Future. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.56/77

57 Algorithmic Advances in 1990 s 1992 LQCD perturbation theory Effective field theory (e.g., NRQCD, Fermilab) Improved discretizations larger a Improved staggered/naive quarks: Det(D γ + m) > 0 as in continuum (small m okay). Flavor-changing perturbative remove systematically. Naive quarks simple analyses, operators. No O(a) errors and much faster unquenching! Lattice QCD is in revolution: 100 % errors in % errors today for wide range of masses, form factors % possible now and in next few years.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.57/77

58 High-Precision Possible Now Few % accuracy for gold-plated calculations: (Cornell Workshops, 2001 and 2002) Masses, decay constants, semileptonic form factors, and mixing amplitudes for D, D s, D, D s, B, B s, B, B s, and baryons. Masses, leptonic widths, electromagnetic form factors, and mixing amplitudes for any meson in ψ/υ families below D/B threshold. Masses, decay constants, electroweak form factors, charge radii, magnetic moments and mixing for low-lying light-quark hadrons. High-precision masses and amplitudes with at most one hadron in the initial and/or final state, for stable or nearly stable hadrons (Γ < MeV).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.58/77

59 New collaboration (HPQCD): M. Alford, C. Davies (Glasgow) A. El-Khadra (Illinois) S. Gottlieb (Indiana) R. Horgan (Cambridge) K. Hornbostel (SMU) A. Kronfeld, P. Mackenzie, J. Simone (Fermilab) P. Lepage (Cornell) J. Shigemitsu (OSU) H. Trottier (SFU) R. Woloshyn (TRIUMF) + working closely with MILC Collaboration. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.59/77

60 Uses current techniques. Progress driven by improved methods. Future pace will be much faster than pace of hardware evolution.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.60/77

61 HPQCD Plan Compute dozens (?) of gold-plated quantities to few percent over next few years. Unquenched n f = 6 with improved staggered quarks. NRQCD and Fermilab actions for c, b quarks through v 6. Actions, operators corrected through order a 2, 1/M 2. One and two-loop perturbation theory (automated). PC cluster is optimal (simulations, pert n theory... ).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.61/77

62 HPQCD Plan Focus on B and D physics maximum impact on experimental community (BaBar, Belle, CLEO... ). Gold-plated quantities for every off-diagonal CKM element. V ud V us V ub π lν K πlν B πlν V cd V cs V cb D lν D s lν B Dlν D πlν D Klν V td V ts V tb B d B d B s B s Extensive cross-checks for error calibration: Υ, ψ, B, D, K, π..... G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.62/77

63 HPQCD So far... Automated one-loop perturbation theory. Λ V /Λ latt for improved gluons. f π and f K, B K, and m s. Flavor-changing in naive/staggered quarks. Anisotropy and speed of light on anisotropic lattices. Tree-level spin-independent NRQCD through v 6 and spin-dependent through v 8 ; one-loop soon. Operator design with naive quarks. High-β techniques for nonperturbative perturbation theory. Constrained/Bayesian curve fitting.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.63/77

64 Very preliminary tunings/results: HPQCD+MILC collaborations. n f = 3, a = 1/8 fm. Tune m u =m d, m s, m c, m b and α s using m π, m K, m ψ, m Υ, and E Υ (1P 1S). α MS (M Z ) = (4) m s (2 GeV) = 80 (20) MeV Errors reduced 3 4 by Fall 02.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.64/77

65 New results: (lattice QCD)/(experiment) Now (n f = 3) Before 2000 (n f = 0) f K f π 2M Bs M Υ ψ(1p 1S) Υ(2P 1S) Υ(3S 1S) Υ(2S 1S) LQCD/Exp t LQCD/Exp t 1.3 HPQCD+MILC: Very Preliminary. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.65/77

66 HPQCD case study: f D errors Perturbation theory: Connects lattice to continuum (fills in gaps): for f D use J cont = Z J latt + a J where Z = 1 + c 1 α s (µ) + c 2 αs 2 + and µ 2/a is typical (for α V and n f = 3). Current work uses 1 st -order results; relative error is O(αs) 2 7% for a = 0.1 fm. This is the dominant error. Next generation will use 2 nd -order results, giving relative errors of O(αs) 3 1.6% at a = 0.1 fm.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.66/77

67 HPQCD case study: f D errors Finite-lattice spacing errors: E.g., on lattice p 2 (sin(pa)/a) 2 = p 2 ( 1 (pa) 2 /3 + ). Remove a, a 2... errors (improved discretizations). (pa) 2 /3 0.7% for p 300 MeV and a = 0.1 fm. O(a 2 ) improvement crucial for high-momentum form factors, and for suppressing flavor-changing interactions.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.67/77

68 HPQCD case study: f D errors 1/M errors: Effective field theory (e.g., NRQCD) essential for heavy quarks 1/M expansion. Current work accurate through O(1/M) errors: O(1/M 2 ) 2% or less for f D ; O(α s /M) 3.6% for f D ; 3 10 times smaller for B mesons. Future work accurate through O(α s /M, 1/M 2 ); relative error is O(αs/M) 2 0.9%.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.68/77

69 HPQCD case study: f D errors Unquenching: Most past work is quenched: m u,d,s for sea quarks (i.e., no vacuum polarization) errors of 10 20%. Current simulations use realistic m s and m u,d = m s /5, m s /7.... Chiral perturbation theory error estimates/corrections. Relative errors = O(15% (m u,d /m s ) 2 ) 1% for m u,d = m s /5. Complicated by flavor-changing interactions ( couple %?). Simulations with a = 0.1 fm, n f = 6, m u,d = m s /4 require 3 months on 200-node PC cluster for 1% statistical errors. Use improved staggered quarks. Lots of n f = 3 gluon configurations already (MILC). No more quenched analyses!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.69/77

70 HPQCD case study: B πlν B πlν V ub but... (p l + p ν ) 2 0 p π 2.5 GeV need a GeV = 0.08 fm computers 3 7 larger.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.70/77

71 Or use mnrqcd (moving NRQCD): a) Choose frame where B moves share momentum between B and π. b) Parameterize b-quark s momentum p µ b M b u µ B + kµ 4-velocity of B meson. k (Λ/M b ) p b p b where Λ 0.5 GeV. discretize k but treat M b u µ B exactly. N.B. Best frame has p B 8 GeV and p π k ΛM b /2 0.8 GeV. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.71/77

72 mnrqcd lagrangian: L mnrqcd = χ ( id t + iv D + 1 2mγ ( D 2 (v D) 2 + σ B ) ) + χ where B = γ ( B v E γ ) γ + 1 v v B. Hashimoto and Matsufuru (1996); Sloan (1998); Foley et al (2002); c.f. HQET.. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.72/77

73 Challenge for lattice QCD Demonstrate reliability at the level of 1 3% errors, given past history of 10 20% errors. Requires comparison with wide variety of highly accurate experimental data. High precision differentiate QCD from models. Wide variety independent tests of all components. Must test: Heavy-quark actions (NRQCD, Fermilab, etc.). Light-quark actions (improved stagg. quarks). Gluon action. High-order perturbation theory. Techniques for computing spectra, form factors..... G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.73/77

74 A problem for lattice QCD There is very little high-precision QCD data from experiment. Solution: new CLEO-c experiment!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.74/77

75 CLEO-c: High-Precision QCD 2002 Υ family: Masses, spin splittings, widths, form factors, mixing... to few %. Richest testing ground for heavy-quark actions independent calibration/test of b-quark action used in B simulations. Overconstrain b-quark action. 2004/5 D, D s mesons: Leptonic, semileptonic widths and form factors to few %. Calibrate LQCD on analogues of crucial B processes. V cd and V cs to few %, new unitarity triangles, new physics (?) ψ/j family, glueball spectrum. LQCD in race to predict CLEO-c results!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.75/77

76 Conclusion Superb opportunity for LQCD to have an impact on particle physics. LQCD essential to high-precision B/D physics at BaBar, Belle, CLEO-c... Predicting CLEO-c, BaBar/Belle results much-needed credibility for LQCD. Landmark in history of quantum field theory: quantitative verification of nonperturbative technology (c.f., 1950 s). Ready for beyond the Standard Model!. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.76/77

77 CKM today and with 2 3% theory errors. And with B Factories... 95% confidence levels; CLEO-c (2001).. G.P. Lepage, High Precision Nonperturbative QCD at the SLAC Summer Institute (August 2002). p.77/77